## ENEE324 Engineering Probability

Course Description: This course covers basic probability theory: axioms of probability, discrete and continuous random variables, pairs of random variables, random vectors; marginal, joint, conditional and cumulative probability distributions, moment generating functions, expectations, and correlations. Also covered are sums of random variables, central limit theorem, sample mean, parameter estimation via sample mean and confidence intervals.

Prerequisite(s) [4]: ENEE322; completion of all required 200-level ENEE courses

Corequisite(s): None

Course Objectives:

• Understand the basic rules for manipulating probability densities in the computation of event probabilities, functions of random variables and expected values
• Understand pairs of random variables, random vectors and their marginal, joint and conditional probability distributions, conditional expectations
• Understand concepts of correlation and independence
• Understand sums of random variables, use of moment generating functions, central limit theorem
• Understand how means can be estimated using the sample mean; understand confidence intervals

Topics Covered:

• Sample space and events
• Axioms of probability
• Computing probabilities
• Conditional probability and independence
• Sequential experiments
• Random variables
• Some important random variables
• Functions of a random variable and expected value
• Moment generating functions
• Multiple random variables
• Joint, marginal and conditional probability distributions
• Conditional expectation
• Covariance, correlation matrices
• Functions of multiple random variables
• Sums of independent random variables
• Central limit theorem
• Sample mean
• Introduction to parameter estimation via sample mean, confidence intervals

[4] Credit only granted for: BMGT231, STAT400 or ENEE324. Additional information: Electrical Engineering and Computer Engineering majors may not substitute STAT400 for ENEE324.